In this paper two basic SQP-approaches for solving implicitly defined inverse problems are presented. Such problems often arises in parameter identification for differential equations. We also include regularization strategies which differ from similar problems in Optimal control. The main focus is on formulating saddle point problems for calculating the next iterate. Conditions for the unique and stable solvability of these problems are presented. The analytical considerations are illustrated by two examples including their discretizations and a numerical case study.

Dans les situations convexes, le problème d'optimisation globale peut être abordé par un ensemble de méthodes classiques, telles, par exemple, celles basées sur le gradient, qui ont montré leur efficacité en ce domaine. Lorsque la situation n'est pas convexe, ces méthodes peuvent être mises en défaut et ne pas trouver un optimum global. La contribution de cette thèse est une méthodologie pour la détermination de l'optimum global d'une fonction non convexe, en utilisant des algorithmes hybrides basés sur un couplage entre des algorithmes stochastiques issus de familles connues, telles, par exemple, celle des algorithmes génétiques ou celle du recuit simulé et des algorithmes déterministes perturbés aléatoirement de façon convenable. D'une part, les familles d'algorithmes stochastiques considérées ont fait preuve d'efficacité pour certaines classes de problèmes et, d'autre part, l'adjonction de perturbations aléatoires permet de construire des méthodes qui sont en théorie convergents vers un optimum global. En pratique, chacune de ces approches a ses limitations et insuffisantes, de manière que le couplage envisagé dans cette thèse est une alternative susceptible d'augmenter l'efficacité numérique. Nous examinons dans cette thèse quelques unes de ces possibilités de couplage. Pour établir leur efficacité, nous les appliquons à des situations test classiques et à un problème de nature stochastique du domaine des transports.

This study aims to evaluate the use of mathematical optimisation algorithms for the optimisation of a vehicle’s spring and damper characteristics, with respect to ride comfort and handling. Traditionally the design of a vehicle’s suspension spring and damper characteristics are determined by a few simple planar model calculations, followed by extensive trial-and-error simulation or track testing. With the current advanced multi-body dynamics computer software packages available to the design engineer, the integration of traditional mathematical optimisation techniques with these packages, can lead to much faster product development. This, in turn results in a reduction of development costs. A sports utility vehicle is modelled by means of a general-purpose computer programme for the dynamic analysis of a multi-body mechanical system. This model is validated against measurements from road tests. The mathematical model is coupled to two gradient-based mathematical optimisation algorithms. The performance of the recently proposed Dynamic-Q optimisation algorithm, is compared with that of the industry-standard gradient based Sequential Quadratic Programming method. The use of different finite difference approximations for the gradient vector evaluation is also investigated. The results of this study indicate that gradient-based mathematical optimisation methods may indeed be successfully integrated with a multi-body dynamics analysis computer program for the optimisation of a vehicle’s suspension system. The results in a significant improvement in the ride comfort as well as handling of the vehicle. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2006. / Mechanical and Aeronautical Engineering / unrestricted

This thesis presents the development and implementation of a generalized optimization framework for use in sheet-stamping process simulation by finite element analysis. The generic framework consists of three main elements: a process simulation program, an optimization code, and a response filtering program. These elements can be filled by any combination of applicable software packages. Example sheet-stamping process simulations are presented to demonstrate the usage of the framework in various forming scenarios. Each of the example simulations is presented with a sensitivity analysis. These examples include analysis of a 2-dimensional single-stage forming, a 2-dimensional multi-stage forming, and two different 3-dimensional single-stage forming processes. A forming limit diagram is used to define failure in the 3-dimensional process simulations. Optimization results are presented using damage minimization, thinning minimization, and springback minimization with aluminum alloy 6061-T6 blanks.

Sambandsanalys av surveydata kompliceras av förekomsten av slumpfel och metodeffekter i de avgivna svaren. Dessa felkällor kan leda till betydande över- eller underskattning av sambanden mellan undersökta variabler, och riskerar att leda till felaktiga slutsatser. En sedan länge känd metod för att estimera och kontrollera för slumpfel och metodeffekter i enkätdata är den så kallade Multitrait Multimethod-metoden (MTMM). Nackdelen med MTMM-metoden är att den kräver att varje fråga som ska analyseras ställs minst tre gånger i samma enkät, vilket gör att ansatsen i praktiken oftast inte är möjlig att tillämpa. Sedan 2012 finns dock ett verktyg, SQP 2.0, som gör det möjligt att skatta slumpfel och metodeffekter i enkätdata utan att genomföra MTMM-experiment. Den här uppsatsen utvärderar prediktionerna från SQP 2.0 på en enkät om arbetslivsrelaterade frågor besvarad av svenska och brittiska respondenter. Programvarans prediktioner jämförs med resultat från MTMM-experiment, och effekten på sambandsanalysen av att tillämpa SQP-programvarans prediktioner av slumpfel och metodeffekter studeras. Slutsatserna från studien är att SQP 2.0 ger predicerade värden för slumpfel och metod-effekter som ligger nära de MTMM-estimerade i de flesta fall, men att betydande avvikelser också förekommer. Vidare konstateras att korrigering för slumpfel och metodeffekter har en betydande effekt på absolutvärdet av korrelationerna mellan variabler under de studerande förhållandena: korrelationerna i det studerade fallet ökar kraftigt efter justering. Korrelationernas relativa storlek förändras i mindre utsträckning, men för en enkät med mer varierade frågetyper kan också dessa påverkas kraftigt. / Correlation analysis of survey data is complicated by the presence of random errors and method effects in the answers given. These factors can lead to significant over- or underestimation of the correlations between variables. A well-established method for estimating and controlling for random error and method effects in survey data is the Multitrait-Multimethod (MTMM) approach. The disadvantage of this method is that it requires that each survey item to be analysed is asked multiple times in the same survey, making the approach hard to use in many practical situations. Since 2012 there is a tool available, SQP 2.0, to predict random errors and method effects in survey data without performing MTMM experiments. This paper evaluates the use of predictions from the SQP 2.0 software on the correlation analysis of a survey of work related matters answered by Swedish and British respondents. The software's predictions are compared with results from MTMM experiments, and the effect on the correlations of applying the SQP software's predictions of random errors and method effects are studied. The conclusion of the study is that SQP 2.0 gives predicted values for random error and method effects that are close to the MTMM-estimates in most cases, but that considerable deviations also occur. It is further concluded that controlling for random error and method effects has a significant effect on the absolute values of the correlations between variables in the studied cases: the correlations in the study increase substantially after adjustment. The relative sizes of the correlations between variables change to a lesser extent, but a questionnaire with more varied question types may have lead to different results in this respect.

Cette thèse traite le développement d'un modèle mathématique d'optimisation acoustique des trajectoires de vol de deux avions commerciaux en approche sous contrainte énergétique, aérodynamique et opérationnelle. C'est un modèle analytique de contrôle optimal non-linéaire et non-convexe régi par un système d'équations différentielles ordinaires issues de la dynamique de vol et des contraintes associées. Notre contribution porte sur la modélisation mathématique des équations, l'optimisation et la programmation algorithmique d'un modèle d'optimisation non-linéaire du bruit de deux avions en approche simultanée. Les points abordés sont le développement mathématique du modèle 3D «exact» de leur dynamique de vol, la modélisation mathématique de la commande optimale de ce système dynamique, l'introduction de la consommation du carburant par les avions comme une équation différentielle avec une fonction consommation spécifique variable en fonction de l'évolution de leur dynamique, la modélisation mathématique instantanée de la fonction objectif représentant le bruit global des deux avions en approche. Sa résolution porte sur la méthode directe de programmation séquentielle quadratique avec régions de confiance sous AMPL et KNITRO. Une méthode indirecte a été appliquée sous le principe de maximum de Pontryagin suivie d’une discrétisation de type Runge-Kutta partition-née symplectique d'ordre 4 afin de démontrer la commutation entre l'approche directe et l'approche indirecte. Les résultats obtenus confirment des trajectoires optimales en descente continue, réduisant le bruit au sol ainsi que la consommation de kérosène de deux avions / This thesis develops an mathematical non-linear optimization model of flight paths of two aircraft in approach minimizing the perceived noise on the ground while energetic constraint is considered. This is an analytical model of non-linear and non-convex optimal control governed by a system of ordinary differential equations resulting from the dynamics of flight and with their associated constraints. Our contribution focuses on the mathematical modeling equations, optimization and algorithmic programming of an acoustic non-linear optimization model of two aircraft simultaneously on approach. The addressed issues are the mathematical development of the «correct» 3D model, their flight dynamics, the mathematical modeling of the optimal control of dynamic system, the consideration of fuel consumption by aircraft as a differential equation with a consumption function specific variable depending on the evolution of their dynamics, the mathematical modeling of the instantaneous objective function representing the overall noise of the two approaching aircraft. Resolution deals with the direct method of sequential quadratic programming with confidence regions while AMPL programming language and KNITRO are considered. An indirect method was applied under the Pontryagin maximum principle, followed by a Runge-Kutta symplectic partitioned discretization to demonstrate the commutation between the direct approach and indirect approach. The expected results confirm optimal trajectories reducing ground noise and fuel consumption of two aircraft

Dans les situations convexes, le problème d'optimisation globale peut être abordé par un ensemble de méthodes classiques, telles, par exemple, celles basées sur le gradient, qui ont montré leur efficacité en ce domaine. Lorsque la situation n'est pas convexe, ces méthodes peuvent être mises en défaut et ne pas trouver un optimum global. La contribution de cette thèse est une méthodologie pour la détermination de l'optimum global d'une fonction non convexe, en utilisant des algorithmes hybrides basés sur un couplage entre des algorithmes stochastiques issus de familles connues, telles, par exemple, celle des algorithmes génétiques ou celle du recuit simulé et des algorithmes déterministes perturbés aléatoirement de façon convenable. D'une part, les familles d'algorithmes stochastiques considérées ont fait preuve d'efficacité pour certaines classes de problèmes et, d'autre part, l'adjonction de perturbations aléatoires permet de construire des méthodes qui sont en théorie convergents vers un optimum global. En pratique, chacune de ces approches a ses limitations et insuffisantes, de manière que le couplage envisagé dans cette thèse est une alternative susceptible d'augmenter l'efficacité numérique. Nous examinons dans cette thèse quelques unes de ces possibilités de couplage. Pour établir leur efficacité, nous les appliquons à des situations test classiques et à un problème de nature stochastique du domaine des transports. / This thesis concerns the global optimization of a non convex function under non linear restrictions, this problem cannot be solved using the classic deterministic methods like the projected gradient algorithm and the sqp method because they can solve only the convex problems. The stochastic algorithms like the genetic algorithm and the simulated annealing algorithm are also inefficients for solving this type of problems. For solving this kind of problems, we try to perturb stocasicly the deterministic classic method and to combine this perturbation with genetic algorithm and the simulated annealing. So we do the combination between the perturbed projected gradient and the genetic algorithm, the perturbed sqp method and the genetic algorithm, the perturbed projected gradient and the simulated annealing, the Piyavskii algorithm and the genetic algorithm. We applicate the coupled algorithms to different classic examples for concretited the thesis. For illustration in the real life, we applicate the coupled perturbed projected gradient end the genetic algorithm to logistic problem eventuelly transport. In this view, we sold the efficient practices.

Les travaux de cette thèse portent sur la méthodologie de conception des Machines Synchrones à Aimants Permanents (MSAP) avec pour application le véhicule électrique. Dans une première partie, nous avons abordé du contexte de l'étude et de la problématique du dimensionnement. A l'occasion, nous avons montré qu'il est nécessaire d'adopter une méthodologie de design appropriée en fonction de l'avancement de chaque projet dans le cadre du processus de conception. Nous avons alors proposé différents niveaux de modélisation afin de repérer la machine optimale face au cahier des charges pour ensuite la caractériser plus finement et l'optimiser. La seconde partie du rapport traite donc de la modélisation et de l'optimisation de la MSAP. En premier lieu, un modèle analytique permet d'évaluer les performances globales des centaines de machines très rapidement. Ce premier calcul permet de sélectionner les meilleures machines à l'application pour ensuite les optimiser. Puis, le second niveau de modélisation se base sur les réseaux de réluctances. Ce niveau plus fin permet d'une part de retrouver les performances affinées des MSAP et également de procéder à l'optimisation. Enfin, la dernière partie du rapport est consacrée à l'optimisation de la MSAP en vue d'améliorer grandement les performances et de satisfaire au mieux au cahier des charges.

Neste trabalho o autor programa e avalia algoritmos para análise e otimização de pressão sonora desenvolvidos para sistemas acoplados vibroacústicos, verificando o desempenho da análise da resposta e comparando a adequação dos algoritmos de Programação Quadrática Sequencial (SQP - Sequencial Quadratic Programming) e Genético na otimização da resposta. A otimização da resposta é implementada no programa acadêmico de elementos finitos Meflab, e utiliza para otimização a função fmincon disponível no programa comercial Matlab®. Igualmente a otimização da resposta é implementada através de um código desenvolvido de algoritmos genéticos. Para os casos acoplados estudados o algoritmo SQP mostra uma redução da pressão sonora inicial inferior ao algoritmo Genético, para casos desacoplados o método SQP consegue reduções maiores. Os resultados foram validados através de formulações analíticas disponíveis e comparados em alguns casos com soluções de programas comerciais. / In this work the author implements in a software and evaluates algorithms for analysis and optimization of the sound pressure developed for coupled vibroacoustic systems, checking the performance and response analysis comparing the suitability of the Sequencial Quadratic Programming (SQP) and Genetic algorithms in optimizing response. The optimization of the response is implemented in the academic program Meflab finite element, and uses optimization function fmincon available in the commercial program Matlab ®. Also the optimization of the response is implemented through a code developed genetic algorithms. For the coupled cases studied the SQP algorithm recduce less the inicial sunde pressure tha Genetic algorithm, for uncoupled cases SQP method has a bigger reduccion. The results were validated by analytical formulations available in some cases and compared with commercial software solutions.

Neste trabalho o autor programa e avalia algoritmos para análise e otimização de pressão sonora desenvolvidos para sistemas acoplados vibroacústicos, verificando o desempenho da análise da resposta e comparando a adequação dos algoritmos de Programação Quadrática Sequencial (SQP - Sequencial Quadratic Programming) e Genético na otimização da resposta. A otimização da resposta é implementada no programa acadêmico de elementos finitos Meflab, e utiliza para otimização a função fmincon disponível no programa comercial Matlab®. Igualmente a otimização da resposta é implementada através de um código desenvolvido de algoritmos genéticos. Para os casos acoplados estudados o algoritmo SQP mostra uma redução da pressão sonora inicial inferior ao algoritmo Genético, para casos desacoplados o método SQP consegue reduções maiores. Os resultados foram validados através de formulações analíticas disponíveis e comparados em alguns casos com soluções de programas comerciais. / In this work the author implements in a software and evaluates algorithms for analysis and optimization of the sound pressure developed for coupled vibroacoustic systems, checking the performance and response analysis comparing the suitability of the Sequencial Quadratic Programming (SQP) and Genetic algorithms in optimizing response. The optimization of the response is implemented in the academic program Meflab finite element, and uses optimization function fmincon available in the commercial program Matlab ®. Also the optimization of the response is implemented through a code developed genetic algorithms. For the coupled cases studied the SQP algorithm recduce less the inicial sunde pressure tha Genetic algorithm, for uncoupled cases SQP method has a bigger reduccion. The results were validated by analytical formulations available in some cases and compared with commercial software solutions.